Right-angled triangle vertices = parallelogram

Hello,

The question asks us to draw a triangle ABC. It then asks us to construct a right-angle isosceles triangle with Hypotenuse AB and its 3rd vertex, R, lying entirely inside the triangle ABC. It then asks us to construct an isosceles right-angle triangle with hypotenuse BC lying entirely outside of ABC, 3rd vertex P, and the same with Hypotenuse AC lying entirely outside triangle ABC, with 3rd vertex Q.
The question asks us to show that CQRP is a parallelogram.

So I am not sure where to start. I know the most useful property of a parallelogram here would be that opp angles are equal but I have had no luck in starting a solution - i.e. there are no obvious similar triangles.
A starter would be much appreciated
Thank you

Re: Right-angled triangle vertices = parallelogram

Originally Posted by Cheesemongergee

Hello,

The question asks us to draw a triangle ABC. It then asks us to construct a right-angle isosceles triangle with Hypotenuse AB and its 3rd vertex, R, lying entirely inside the triangle ABC. It then asks us to construct an isosceles right-angle triangle with hypotenuse BC lying entirely outside of ABC, 3rd vertex P, and the same with Hypotenuse AC lying entirely outside triangle ABC, with 3rd vertex Q.
The question asks us to show that CQRP is a parallelogram.

So I am not sure where to start. I know the most useful property of a parallelogram here would be that opp angles are equal but I have had no luck in starting a solution - i.e. there are no obvious similar triangles.
A starter would be much appreciated
Thank you

It seems you are rephrasing the question, May I ask you to reproduce the question as it is written in your textbook.